Chemical Thermodynamics | General Chemistry 3
Spontaneity of Reactions
Spontaneous process: a process that takes place without the input of energy from an external source
It generally leads to a decrease in the energy of the system ⇒ a spontaneous process is very often exothermic. But it's not always the case
2 H2 (g) + O2 (g) → 2 H2O (l) is a spontaneous process
ΔH0rxn = - 571.6 kJ.mol-1 < 0 ⇒ exothermic reactionH2O (s) → H2O (l) is a spontaneous process at T > 0°C
ΔH0fus = +6.0 kJ.mol-1 > 0 ⇒ not exothermic reaction
Law of Thermodynamics
First Law of Thermodynamics:
The energy of the universe is constant ⇒ energy can neither be created nor destroyed
ΔUuniv = ΔUsys + ΔUsurr = 0
⇒ ΔUsys = - ΔUsurr = q + w
Second Law of Thermodynamics:
The total entropy of an isolated system can never decrease over time and is constant if all processes are reversible
⇒ the entropy change is never negative: ΔSsystem + ΔSsurrounding 0
(ΔSsystem + ΔSsurrounding = 0 for an equilibrium)
Entropy S (in J.K-1): measure of the amount of disorder in a system (ex: expansion of a gas into a vacuum)
ΔSsys
ΔSsys = entropy change (in J.K-1)
qsys = heat (in J)
Tsys = temperature (in K)
Entropy change
Entropy change on fusion:
ΔSfus =
ΔSfus = molar entropy of fusion (in J.K-1.mol-1)
ΔHfus = molar enthalpy of fusion (in J.mol-1)
Tm = melting point (in K)
Entropy change on vaporization:
ΔSvap =
ΔSvap = molar entropy of vaporization (in J.K-1.mol-1)
ΔHvap = molar enthalpy of vaporization (in J.mol-1)
Tb = boiling point (in K)
Entropy Changes for Reactions
Standard entropy change ΔS0rxn for a chemical reaction (in J.K-1.mol-1):
ΔS0rxn = αi S0 [products] - αi S0 [reactants]
αi = stoichiometric coefficient
S0 = standard entropy (in J.K-1.mol-1)
a A + b B → c C
ΔS0rxn = c S0 [C] – a S0 [A] – b S0 [B]N2 (g) + 3 H2 (g) 2 NH3 (g)
ΔS0rxn = 2 S0 [NH3] – S0 [N2] – 3 S0 [H2]
Gibbs Energy Change and Spontaneity of Reactions
Gibbs energy change ΔGrxn (in J.mol-1):
ΔGrxn = ΔHrxn - TΔSrxn
ΔHrxn = enthalpy change (in J.mol-1)
ΔSrxn = entropy change (in J.K-1.mol-1)
T = temperature (in K)
Gibbs criteria for reaction spontaneity:
- If ΔGrxn < 0: reaction is spontaneous and additional products can form
- If ΔGrxn > 0: reaction is not spontaneous ⇒ Input of energy from an external source is necessary to form additional products
- If ΔGrxn = 0: reaction is at equilibrium
Gibbs Energy Change and Reaction Quotient
ΔGrxn = RT ln
R = ideal gas constant = 8.314 J.mol-1.K-1
T = temperature (in K)
Q = reaction quotient
K = equilibrium constant
If Q > K ΔGrxn > 0: reaction proceeds spontaneously from right to left
If Q < K ΔGrxn < 0: reaction proceeds spontaneously from left to right
If Q = K ΔGrxn = 0: reaction is at equilibrium
A reversible chemical reaction has reached equilibrium when the Gibbs free energy Grxn reaches a minimum
Relationship between ΔG and ΔG°
Standard Gibbs energy change ΔG0rxn for a reaction (in J.mol-1):
ΔG0rxn = - RT ln K
R = ideal gas constant = 8.314 J.mol-1.K-1
T = temperature (in K)
K = equilibrium constant
ΔGrxn = RT ln = RT ln Q – RT ln K:
ΔGrxn = ΔG0rxn + RT ln Q
R = ideal gas constant = 8.314 J.mol-1.K-1
T = temperature (in K)
Q = reaction quotient
Gibbs Energies of Formation
Standard Gibbs energy ΔG0rxn for a chemical reaction (in J.mol-1):
ΔG0rxn = αi ΔG0f [products] - αi ΔG0f [reactants]
αi = stoichiometric coefficient
ΔG0f = standard molar Gibbs energy of formation
(in J.mol-1)
a A + b B → c C
ΔG0rxn = c ΔG0f [C] – a ΔG0f [A] – b ΔG0f [B]N2 (g) + 3 H2 (g) 2 NH3 (g)
ΔG0rxn = 2 ΔG0f [NH3] – ΔG0f [N2] – 3 ΔG0f [H2]
Van’t Hoff and Clapeyron-Clausius Equations
ΔG0rxn = ΔH0rxn – TΔS0rxn and ΔG0rxn = - RT ln K
⇒ ln K = - +
⇒ a plot of ln K versus is linear with slope - and intercept
van’t Hoff Equation:
ln = x = x
Clapeyron-Clausius Equation:
ln = x = x